@Starfall @amWhy @BrevanEllefsen Good thing I don't care about what you guys care about what other people do to other people who care about things in different ways relating to other people about...
Last night I had a dream where I needed to find all the poles of $\frac{x^n}{1-x^s}$ so that I could calculate $\int_0^x \frac{t^n}{1-t^s} dt$. I doubt this approach would work in the slightest, but I wonder why I dreamed it.
@BrevanEllefsen I've probably been teaching you too much complex analysis
Indeed, that approach does actually work if you were trying to solving the following integral: $$P.V.\int_0^{+\infty}\frac{x^n}{1-x^s}~dx$$
@SimplyBeautifulArt Haha. I would hardly say that it's you who has gotten me into complex analysis either, though I liked the humor XD I'm read through pieces of a couple PDFs and I should have a textbook coming on March 7th
@SimplyBeautifulArt is there a known solution for variable upper index?
I was recently looking through integration techniques when I came upon differentiation under the integral sign (DUIS). It seems to be pretty powerful, for example:
$$f(t)=\int_0^1\frac{x^t-1}{\ln(x)}\ dx\implies f'(t)=\int_0^1x^t\ dx=\frac1{t+1}\\\implies f(t)=C+\ln(t+1)\\f(0)=0\implies C=0\\\i...
Note that substituting $x=e^{-t}$, your integral becomes $$\int_0^1 \frac{x^3-1}{\ln x}\mathrm{d}x=\int_{0}^{\infty} \frac{e^{-t}-e^{-4t}}{t} \mathrm{d} t$$
As $\ln x =-t$. Now use Frullani's Integral to get that $$\int_{0}^{\infty} \frac{e^{-t}-e^{-4t}}{t} \mathrm{d} t=\ln 4$$
As corroborated...
i don't agree with most of what ernest w. adams writes, in fact, i don't think ernest w. adams has written a single answer that i can recommend or cite without reservation
@S.C.B. i am not sure who said this, but someone once made this remark: "the status quo is that liberals mostly read left leaning newspapers, and conservatives mostly read right leaning newspapers; but if you look at it logically, it should be the exact opposite"
@user21820 on any given issue, my trust in a specific institution is inversely proportional to my perception of how much incentive they would have to lie about a specific topic
with different topics, i trust different institutions
turkey is in bad shape economically right now, and there's still a climate of uncertainty before the referendum on the recent constitutional changes
the USD/TRY ratio has been declining recently, which is a good sign
the attempted coup is only related to the (still ongoing) purge
it is being conducted with extremely sloppy standards, and as broadly as possible; but hopefully the people who have been rather absurdly accused for no reason will be exonerated once the trials begin
turkey doesn't have the luxury of purging its judiciary without a care in the world right now, they need all the judges and prosecutors they can find
@S.C.B. i don't see how the election was good for CNN
if anything, it was very bad for CNN, and it continues to be very bad for CNN
Notice that
$$\left.\int_1^xt^ndt=\frac{t^{n+1}}{n+1}\right|_1^x=\frac{x^{n+1}-1}{n+1}$$
but at $n=-1$, we get division by $0$, and clearly this is bad. However, following this line of logic, we can take the limit as $n\to-1$ to get
$$\int_1^x\frac1tdt\stackrel?=\lim_{n\to-1}\frac{x^{n+1}-1}{...
It's the condemnation of a world religion, in its entirey, and evangelizing its evilness (recruiting extremists to believe your extremism, through offensive language and fake news, and cannot be justified as political, that violates site/chat rules.
This is sort of a follow-up to two past discussions:
Toward a philosophy of Chat
Does the Be Nice policy require SE users to "be nice" to people who are not SE users (e.g. public figures)?
Over the past year, there's been an uptick in discussions of politics in chat. JUST LOOK AT THIS CHART!
...
Someone tells you a topic - or the way you're discussing it - is being bothersome, that's a good time to either drop it or take it into a different room.
@Mithrandir ...and nobody said anything about how the subject was inappropriate - whoever was flagging those messages could surely simply say "i think this subject is inappropriate, could you take this discussion somewhere else?"
@Shog9 i am going to go ahead and say that i did not show any sort of disrespect towards anyone who disagreed with me in that discussion
@Mithrandir also, are you saying that offending people is against the rules?
Someone tells you a topic - or the way you're discussing it - is being bothersome, that's a good time to either drop it or take it into a different room.
@ThomasWard i don't particularly mind if i am suspended or not, i am trying to get you to understand that the way you deal with these "infractions" is fundamentally flawed
that was the whole point of my "suspend your own account" message, but it appears that this point was not delivered very well
We're trying to avoid offending people here, and trying to keep the place friendly for everyone. If you're insulting my religion, I don't feel comfortable - same with political discussions.
It violates the "Be Nice" rules. Which we enforce. We being all moderators.
You've been told to knock it off with the drama. By many people with the capacity and requirement to enforce "be nice". You violate that rule at your own risk. (So, knock it off, and don't keep going with drama)
@Mithrandir you have successfully coerced me into not even being able to say what i think about this policy, because you are implying that if i do, i will be banned; so criticizing site policy in this chat is not allowed either, it seems
@Mithrandir because it's not possible for you to make the experience pleasant for everyone, you're making it extremely unpleasant for me right now; and this will be so for anyone who wants to speak his mind about a controversial issue in one of these chatrooms
This is sort of a follow-up to two past discussions:
Toward a philosophy of Chat
Does the Be Nice policy require SE users to "be nice" to people who are not SE users (e.g. public figures)?
Over the past year, there's been an uptick in discussions of politics in chat. JUST LOOK AT THIS CHART!
...
@SimplyBeautifulArt Maybe you should read posts more carefully before replying with "lmao" and such, lest such replies are taken as support for offensive comments in "your" realm. From now on I'll take your "lmao" or "lol" or :D etc, in response to comments left here, as a stamp of approval and/or agreement from you wrt others' comments. If you simply don't want to acknowledge offensive comments, then ignore them, just don't use lol as a method of avoiding them.
I was recently looking through integration techniques when I came upon differentiation under the integral sign (DUIS). It seems to be pretty powerful, for example:
$$f(t)=\int_0^1\frac{x^t-1}{\ln(x)}\ dx\implies f'(t)=\int_0^1x^t\ dx=\frac1{t+1}\\\implies f(t)=C+\ln(t+1)\\f(0)=0\implies C=0\\\i...
Note that substituting $x=e^{-t}$, your integral becomes $$\int_0^1 \frac{x^3-1}{\ln x}\mathrm{d}x=\int_{0}^{\infty} \frac{e^{-t}-e^{-4t}}{t} \mathrm{d} t$$
As $\ln x =-t$. Now use Frullani's Integral to get that $$\int_{0}^{\infty} \frac{e^{-t}-e^{-4t}}{t} \mathrm{d} t=\ln 4$$
As corroborated...
This is sort of a follow-up to two past discussions:
Toward a philosophy of Chat
Does the Be Nice policy require SE users to "be nice" to people who are not SE users (e.g. public figures)?
Over the past year, there's been an uptick in discussions of politics in chat. JUST LOOK AT THIS CHART!
...
This is the Realm of Simply Beautiful…
This is the Realm of Simply Beautiful…